Exponential Functions

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What is an exponential function?

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An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive number), and 'x' is the exponent.

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What does 'growth' mean in exponential functions?

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Growth in exponential functions refers to a situation where the value increases rapidly over time, typically when the base 'b' is greater than 1.

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What does 'decay' mean in exponential functions?

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Decay in exponential functions refers to a situation where the value decreases over time, typically when the base 'b' is between 0 and 1.

Front

What is the common ratio in an exponential sequence?

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The common ratio is the factor by which we multiply to get from one term to the next in an exponential sequence.

Front

What does the 'a' represent in the equation y = a(b^x)?

Back

In the equation y = a(b^x), 'a' represents the initial value or the y-intercept of the function.

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What is the base in an exponential function?

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The base is the number that is raised to a power in an exponential function, determining the rate of growth or decay.

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How do you identify if a graph is exponential?

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A graph is exponential if it shows a curve that rises or falls sharply, rather than a straight line.

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What is the formula for exponential growth?

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The formula for exponential growth is y = a(1 + r)^t, where 'r' is the growth rate and 't' is time.

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What is the formula for exponential decay?

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The formula for exponential decay is y = a(1 - r)^t, where 'r' is the decay rate and 't' is time.

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What is an example of an exponential growth situation?

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An example of exponential growth is population growth, where the number of individuals increases rapidly over time.